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Crystal Structures and Properties of Iron Hydrides at High Pressure

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Crystal Structures and Properties of Iron Hydrides at High Pressure Crystal Structures and Properties of Iron Hydrides at High Pressure Niloofar Zarifi,y Tiange Bi,y Hanyu Liu,z,{ and Eva Zurek∗,y yDepartment of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260-3000, USA zInnovation Center for Computational Physics Method and Software, College of Physics, Jilin University, Changchun 130012, China {State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun 130012, China E-mail: [email protected] arXiv:1809.08323v1 [cond-mat.supr-con] 21 Sep 2018 1 Abstract Evolutionary algorithms and the particle swarm optimization method have been used to predict stable and metastable high hydrides of iron between 150-300 GPa that have not been discussed in previous studies. Cmca FeH5, P mma FeH6 and P 2=c FeH6 contain hydro- genic lattices that result from slight distortions of the previously predicted I4=mmm FeH5 and Cmmm FeH6 structures. Density functional theory calculations show that neither the I4=mmm nor the Cmca symmetry FeH5 phases are superconducting. A P 1 symmetry FeH7 phase, which is found to be dynamically stable at 200 and 300 GPa, adds another member to the set of predicted nonmetallic transition metal hydrides under pressure. Two metastable phases of FeH8 are found, and the preferred structure at 300 GPa contains a unique 1-dimensional hydrogenic lattice. 2 Introduction The composition and structure that hydrides of iron may assume under pressure has long been of interest to geoscientists. Seismic models suggest that the Earth’s core consists of iron alloyed with nickel and numerous light elements, one of which is suspected to be hydrogen.1 More recently, however, it was proposed that such systems may be a route towards high density bulk atomic hy- drogen.2 The allure of high temperature superconductivity in compressed high hydrides3–6 has been heightened with the discovery of superconductivity below 203 K in a sample of hydrogen sulfide that was compressed to 150 GPa,7 and most recently in studies of the lanthanum/hydrogen 8,9 system . Very high Tc values have been theoretically predicted for many high hydrides includ- 10 11 12 ing CaH6 (235 K at 150 GPa), ScH9 (233 K at 300 GPa), YH6 (264 K at 120 GPa), and 13 LaH10 (286 K at 210 GPa). Moreover, a number of hydrides with intriguing stoichiometries have 14 15 16 recently been synthesized under pressure including LiH6, NaH7, and LaH10. Under pressure the solubility of iron in hydrogen increases17 yielding phases with Fe:H ratios that approach 1:1,18,19 which undergo a number of pressure induced structural phase transitions.20 Evolutionary crystal structure searches coupled with density functional theory (DFT) calculations for FexHy (x; y = 1−4) at 100-400 GPa found a number of unique (meta)stable structures, includ- 21 ing FeH3 in the P m3¯m and P m3¯n spacegroups, as well as P 21=m FeH4. A further theoretical study that focused on the FeH4 stoichiometry found the following sequence of phase transitions: 22 P 213 ! Imma ! P 21=m at 109 and 242 GPa. The superconducting critical temperature, Tc, of the only metallic phase, Imma FeH4, was estimated as being 1.7 K at 110 GPa. Recently, variable-composition evolutionary searches up to 150 GPa found a number of hitherto unknown stable high hydrides of iron including P 4=mmm Fe3H5, I4=mmm Fe3H13, I4=mmm FeH5, and 23 FeH6 with Cmmm and C2=m symmetries. The theoretical study of Bazhanova and co-workers21 inspired experiments by Pepin´ et. al. that resulted in the first synthesis of the higher hydrides of iron under pressure.24 A ferromagnetic I4=mmm FeHx phase with x ∼ 2 formed at 67 GPa, and at 86 GPa further hydrogen uptake yielded a nonmagnetic P m3¯m FeH3 phase. DFT calculations showed that both of the synthesized 3 phases were metallic. Three years later the same group synthesized FeH5 via a direct reaction 2 between iron and H2 above 130 GPa in a laser-heated diamond anvil cell. Powder X-ray diffrac- tion and Rietveld refinement determined that the lattice likely possesses I4=mmm symmetry at 130 GPa. It is composed of layers of quasicubic FeH3 units and atomic hydrogen whose H-H distances resembled those found in bulk atomic hydrogen.2 DFT calculations coupled with evolu- tionary searches verified that I4=mmm FeH5 was thermodynamically stable from 85 GPa up to 23 at least 150 GPa. I4=mmm FeH5 was estimated to be superconducting below ∼50 K around 23,25 23 150 GPa, and the Tc of Cmmm FeH6 was estimated as being 43 K at 150 GPa. However, recent calculations have questioned the conclusions of Refs.,23,25 failing to find superconductivity 26 within I4=mmm FeH5. Herein, we have carried out structure prediction via an evolutionary algorithm (EA) as well as the particle swarm optimization (PSO) technique to find the most stable structures of FeHn (n = 5 − 8) at 150, 200 and 300 GPa. A number of stable or metastable phases that have not been previously discussed are found. Importantly, in agreement with Heil et al.,26 but in disagreement 23,25 with previous reports, we do not find superconductivity in either I4=mmm FeH5 nor in a newly predicted Cmca FeH5 phase. These two dynamically stable, nearly isoenthalpic FeH5 geometries are related by a slight structural distortion that decreases the PV term, but increases the energetic term to the enthalpy of the Cmca geometry as compared to the I4=mmm arrangement. Metastable FeH6, FeH7 and FeH8 phases that could potentially be accessed experimentally are found, and the peculiarities of their structures and electronic structures are discussed. Computational Details The search for stable high pressure structures with FeHn (n = 5 − 8) stoichiometries was carried out using the XTALOPT 27 evolutionary algorithm (EA) (releases 1028 and 1129), and the particle swarm optimization (PSO) algorithm as implemented in the CALYPSO30 code. EA runs were carried out employing simulation cells with 2-8 formula units (FU) at 150, 200 and 300 GPa. 4 In the EA search duplicate structures were detected via the XTALCOMP algorithm.31 PSO runs were performed using cells containing up to 4 FU at 150, 200 and 300 GPa. The lowest enthalpy structures from each search were relaxed in a pressure range from 150 to 300 GPa. Geometry optimizations and electronic structure calculations were performed in the framework of density functional theory (DFT) as implemented in the Vienna Ab Initio Simulation Package (VASP)32,33 with the gradient-corrected exchange and correlation functional of Perdew-Burke- Ernzerhof (PBE).34 The projector augmented wave (PAW) method35 was used to treat the core states, and a plane-wave basis set with an energy cutoff of 600 eV was employed for precise optimizations. The H 1s1 and Fe 2s22p63d74s1 electrons were treated explicitly in all of the cal- culations. The k-point grids were generated using the Γ-centered Monkhorst-Pack scheme, and the number of divisions along each reciprocal lattice vector was chosen such that the product of this number with the real lattice constant was 30 A˚ in the structure searches, and 60-80 A˚ otherwise. Tests carried out on I4=mmm and Cmca FeH5 showed that the k-meshes and energy cutoffs used yielded relative enthalpies that were converged to within ∼0.1 meV/atom . The magnetic moment was calculated for select phases. It was found to be zero, in agreement with previous studies, which found that the high hydrides of iron become nonmagnetic above 100 GPa,23 and that the magnetic 36 moment of I4=mmm FeH2 drops to zero by about 140 GPa. Phonon band structures were calculated using the supercell approach,37,38 or DFT perturbation theory.39 In the former, Hellmann-Feynman forces were calculated from a supercell constructed by replicating the optimized structure wherein the atoms had been displaced, and dynamical matrices were computed using the PHONOPY code.40 The Quantum Espresso (QE)41 program was used to obtain the dynamical matrix and electron-phonon coupling (EPC) parameters. H and Fe pseudopo- tentials, obtained from the QE pseudopotential library, were generated by the Vanderbilt ultrasoft method42 with a 1s1 configuration for H and a 3s23p63d6:54s14p0 valence configuration for Fe. These are the same pseudopotentials used in Ref.25 The PBE generalized gradient approximation was employed. Tests were carried out to confirm that the values calculated for I4=mmm FeH5 at 200 GPa were in agreement with results obtained using PBE-PAW Troullier-Martins potentials43 5 generated by the “atomic” code44 with valence configurations of 1s1 for H and 3s23p63d64s2 for Fe. The critical superconducting temperature, Tc, was estimated using the Allen-Dynes modified McMillan equation,45 where the renormalized Coulomb potential, µ∗, was assumed to be 0.1. Fur- ther details about the dependence of the results on the Gaussian broadening used, as well as the k and q meshes employed, are provided in the SI. Results and Discussion Superconductivity in FeH5? Fig. 1 plots the enthalpies of formation, ∆HF , of the most stable FeHn (n = 5 − 8) compounds that were found via crystal structure prediction (CSP) techniques at 150, 200 and 300 GPa. In a few cases, as discussed in more detail below, the enthalpies of two or more structures differed by only a few meV/atom. Phonon calculations, see Figures S3 and S4 in the SI, were carried out to confirm the dynamic stability of the predicted structures. The phases whose ∆HF lie on the convex hull are thermodynamically stable, whereas those that do not are metastable. At all of the pressures considered only FeH5 lay on the convex hull, regardless of whether the zero-point energy (ZPE) was included in the enthalpy or not.
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